7,077 research outputs found
E(lementary) Strings in Six-Dimensional Heterotic F-Theory
Using E-strings, we can analyze not only six-dimensional superconformal field
theories but also probe vacua of non-perturabative heterotic string. We study
strings made of D3-branes wrapped on various two-cycles in the global F-theory
setup. We claim that E-strings are elementary in the sense that various
combinations of E-strings can form M-strings as well as heterotic strings and
new kind of strings, called G-strings. Using them, we show that emissions and
combinations of heterotic small instantons generate most of known
six-dimensional superconformal theories, their affinizations and little string
theories. Taking account of global structure of compact internal geometry, we
also show that special combinations of E-strings play an important role in
constructing six-dimensional theories of - and -types. We check global
consistency conditions from anomaly cancellation conditions, both from
five-branes and strings, and show that they are given in terms of elementary
E-string combinations.Comment: 58 pages, 16 figures; v2. version to appear in JHE
Continuity argument revisited: geometry of root clustering via symmetric products
We study the spaces of polynomials stratified into the sets of polynomial
with fixed number of roots inside certain semialgebraic region , on its
border, and at the complement to its closure. Presented approach is a
generalisation, unification and development of several classical approaches to
stability problems in control theory: root clustering (-stability) developed
by R.E. Kalman, B.R. Barmish, S. Gutman et al., -decomposition(Yu.I.
Neimark, B.T. Polyak, E.N. Gryazina) and universal parameter space method(A.
Fam, J. Meditch, J.Ackermann).
Our approach is based on the interpretation of correspondence between roots
and coefficients of a polynomial as a symmetric product morphism.
We describe the topology of strata up to homotopy equivalence and, for many
important cases, up to homeomorphism. Adjacencies between strata are also
described. Moreover, we provide an explanation for the special position of
classical stability problems: Hurwitz stability, Schur stability,
hyperbolicity.Comment: 45 pages, 4 figure
F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X
contains information about the abelian sector of the six-dimensional theory
obtained by compactifying F-theory on X. After examining features of the
abelian anomaly coefficient matrix and U(1) charge quantization conditions of
general F-theory vacua, we study Calabi-Yau threefolds with Mordell-Weil
rank-one as a first step towards understanding the features of the Mordell-Weil
group of threefolds in more detail. In particular, we generate an interesting
class of F-theory models with U(1) gauge symmetry that have matter with both
charges 1 and 2. The anomaly equations --- which relate the Neron-Tate height
of a section to intersection numbers between the section and fibral rational
curves of the manifold --- serve as an important tool in our analysis.Comment: 29 pages + appendices, 5 figures; v2: minor correction
Bessel Functions in Mass Action. Modeling of Memories and Remembrances
Data from experimental observations of a class of neurological processes
(Freeman K-sets) present functional distribution reproducing Bessel function
behavior. We model such processes with couples of damped/amplified oscillators
which provide time dependent representation of Bessel equation. The root loci
of poles and zeros conform to solutions of K-sets. Some light is shed on the
problem of filling the gap between the cellular level dynamics and the brain
functional activity. Breakdown of time-reversal symmetry is related with the
cortex thermodynamic features. This provides a possible mechanism to deduce
lifetime of recorded memory.Comment: 16 pages, 9 figures, Physics Letters A, 2015 in pres
An E7 Surprise
We explore some curious implications of Seiberg duality for an SU(2)
four-dimensional gauge theory with eight chiral doublets. We argue that two
copies of the theory can be deformed by an exactly marginal quartic
superpotential so that they acquire an enhanced E7 flavor symmetry. We argue
that a single copy of the theory can be used to define an E7-invariant
superconformal boundary condition for a theory of 28 five-dimensional free
hypermultiplets. Finally, we derive similar statements for three-dimensional
gauge theories such as an SU(2) gauge theory with six chiral doublets or Nf=4
SQED.Comment: 27 page
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